$2500 is invested at 6% compounded quarterly. In how many years will the account have grown to $6000? Round your answer to the nearest tenth of a year.
A) 1.2 years
B) 18.5 years
C) 15.0 years
D) 14.7 years

Question

Quizplus · Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. Here, $A = 6000$, $P = 2500$, $r = 0.06$, and $n = 4$ (since the interest is compounded quarterly). We solve for $t$:$$6000 = 2500(1 + \frac{0.06}{4})^{4t}$$$$2.4 = (1 + 0.015)^{4t}$$$$2.4 = (1.015)^{4t}$$Taking the natural logarithm of both sides:$$\ln(2.4) = 4t \ln(1.015)$$$$t = \frac{\ln(2.4)}{4\ln(1.015)}$$$$t \approx 14.7$$ years.

$2500 Is Invested at 6% Compounded Quarterly